LEN
tontur with the Axis in F ; fo as G D will be to E D in the Ratio of the Sine of the refracted Angle, to the Sine of the Angle of Inclination : (See Refraiiion) So that the Semidiameter and Thicknefs of the Tlano-Convex Lens, with the Ratio or Refraction being given, hence arifes a Method of determining the Focus of parallel Rays ftri- king on the Convex Surface. For
Cor. Hence, if the Letts be Glafs, FD=;C H— | H D. So that if two thirds of the Thicknefs of the Zens be incon- fiderable (as in Practice it ufually happens) parallel Rays meet with the Axis at the Distance of the Diameter from the Zens, even when they ftrike on the Convex Surface.
So that as to the Place of the Focus, 'tis the fame thing whether the plane Surface, or the convex one, be turned to a Luminary of parallel Rays ; tho' it appears both from Experience and trigonometrical Calculation, that there arc more Rays united in a lefs Space, if the convex Surface, than if the plane one be turn'd towards the Sun.
If the Letts v/erc full of Water ED=3CH- 1 H D. Wherefore if \ H D be inconfiderable F D= 3 CH, or if £ H D be inconfiderable F H= 3 C H. Parallel and near Rays, therefore , are united at the Diltancc of half the Di- ameter, if the Refraction be ui Water, even when the Con- vex Surface is oppofed to the luminous Body. Hence, alfo, arifes a Method of determining the Focus of paral- lel Rays ftriking on a Zens Convex on both Sides, the two Semidiameters, and the Thicknefs of the Lens, being given.
On thefe Principles is founded the Structure of refrac- ting Burning-Glafles ; the Sun's Light and Heat being exceedingly augmented in the Focus of a Lens, whether Convex or Piano-Convex : mice the Rays falling pa- rallel to the Axis of the Lens, are reduced into a much narrower Compafs ; fo that 'tis no wonder they burn fome Bodies, melt others, and produce other extraor- dinary Phenomena. See Bnr?ting-Glafs.
If a luminous Body be placed in the Focus behind a Letts, whether Piano-Convex, or Convex on both Sides; or whether equally or unequally, the Rays after Refrac- tion become parallel.
Hence by means of a Convex- Zens, or a little Glafs Bubble full of Water, a very intenfe Light may be pro- jected to a vaft Diftance. . See Mirror.
And this furnifhes us with the Structure of a Lamp or Lanthom, to project an intenfe Light to any immenfe Di- ftance: For a Lens convex on both Sides, being placed op- pofite to a Concave Mirror 5 if in the common Focus of both be placed a lighted Candle, or Wick, the Rays reflected back from the Mirror to the Lens, will be paral- lel to each other j and after Refraction will converge, till they arrive at the Diftance of the Semi-diameter, after which they will again diverge. But the Candle being likewife in the Focus of the Lens, the Rays it throws on the Lens will be parallel : and therefore a very intenfe Light meeting with another equally intenfe, at the Di- ftance of the Diameter from the Lens, the Light will be furprizing : and tho* it afterwards decreafe, yet the pa- rallel and diverging Rays going a long way together, it will be very great at a very great Diftance. -Lanthorns of this kind are of considerable Service in the Night-time to difcover remote Objects, and are ufed with Succefs by Fowlers and Fiftiermen, to gather their Prey together, in order to take them.
If it be required to have the Light at the fame time tranfmitted to feveral Places, as through feveral Streets, £5c. the Number of Lens's and Mirrors are to be encreafed. See Lamp.
If the luminous Body placed in the Focus, be of a large Extent, the Rays flowing from Points fenfibly diftant from each other, can't be parallel, but will conftitute feveral Trains or Pencils of Rays parallel to each other.
The Images of Objects oppoled in any manner to a Convex-Zens, are exhibited^ invertcdly, in its Focus.
Hence if a Paper be applied to a Convex-Zens (effect- ally in a dark Room) at the diftance of its Focus, the Images of Objects filming upon it, will be reprefented diftinctly, and in their natural Colours thereon : Nor is the Focus of the Sun's Rays any thing elfe, in effect, but the Image of the Sun. Hence in Solar F.clipfes, the Sun's Image, eclipfed as it is, may be burnt by a large Zens on a Board, $$c, a very entertaining Phenomenon !
Hence alfo, if a Convex-Lens of any kind, be expofed both to nearer and remoter Objects, and a Paper at the fame time be applied, fo as to receive the Images of Objefts diftinctly, the Diftance of the Focus from the Zens, and thence the Diameter of the Convexity, may be determined.
If a Concave-Mirror be fo placed, as that an inverted Image formed bv Refraction thro' a Lens, be found be- tween the Centre and the Focus, or even beyond the Cen- tre j it will again he inverted by Reflexion, and fo appear erect in the firft Cafe beyond the Untre, and in the lat-
( 442 )
LEN
ter between the Centre and the Focus. On thefe Prin- ciples is built the Camera Obfcura j which fee.
The Diameter of the Image of an Object delineated beyond a Convex-Lais, is to the Object it felf in a Ratio of the Diftance of the Image, to that of the Object.
Since then the Image of a remoter Object, is lefs di- ftant from the Zens, than that of the nearer, the Image of the more remote, will be lefs than that of the nearer. And becaufethe Diftance_of the Image from the Lew* is greater, if the Zens be a Segment of a greater Sphere, than of a lefs ; hence the Image will be greater in the former Cafe than in the latter. The Image therefore will be of fuch a Magnitude, as it would be of, were the Object to fhine into a dark Room thro' a little Hole upon a Wall, at the fame Diftance from the Hole, at which the Focus is from the Zens. When an Object is lefs diftant from a Zens than the Focus of parallel Rays, the Diilance of the Image is greater than that of the Object, other wife the Diilance of the Image is lefs than that of the Object; in the former Cafe, therefore, the Image is greater than the Object, in the latter, lefs.
If the Images be made greater than the Objects, they will not appear diltinctly ; becaufe in that Cale there are fewer Rays which meet after Refraction in the fame Point 5 whence it happens that Rays proceeding from dif- ferent Points of an Object, terminate in the fame Point of an Image, which is the caufe of Confufion. Hence it ap- pears that the fame Aperture of a Lens mayn't be ad- mitted in every Cafe, if we would keep off the Rays which produce Confufion. However, tho'thelmage is then moil diftinct, when no Rays are admitted but thofe near the Axis, yet for want of Rays the Image is apt to be dim.
If the Eye be placed in the Focus ot a Convex-Lens, an Object view'd thro' it, appears erect and enlarg'd, in a Ratio of the Diftance of the Object from the Eye, to that of the Eye from the Lens, if it be near ; but infinitely, if remote. See Micrufcope ; fee alfo Frifm.
For Concave-Lens's, their Laws are as follow.
If parallel Rays ftrike on a flano-Concave-Lens K L, and FC be to F B in the Ratio of the Refraction, the Rays will diverge from the Axis, and the Point of Diver- gency, or Difperfion, call'd the virtual Focus, will be F. (Fig, 3. Flate Of ticks)
For the Ray H 1, parallel to the Axis, is perpendicu- lar to KL, and will therefore pafs unrefracted to E. Wherefore FC being to F B in the Ratio of Refraction, F will be the virtual Focus. See Refraiiion,
If then the Zens be Glafs, F B=2 B C ; i.e. the virtual Focus F will be diftant from the Lens K L by the Space of the Diameter % B C.
If the Refraaion be in Water F B= 3CB5 i.e. the virtual Focus F will be diftant from the Zens K L a Dia- meter and an half 3 B C.
If the Ray A E, parallel to the Axis F P, ftrike on a- Lens Concave on both fides j and both FC be to FB and I P to P H in the Ratio of Refraction : and F P : P H : : F B : B G ; G will be the Point of Difperfion, or the virtual Focus. (Fig. 4. Flate Q pucks)
If therefore ( the Refraction be in a Glafs Lens, the Sums of the Semi- diameters C B and H I, will be to the Diameter of the Concavity of either 2 H I, as the Semi- diameter of the other C B, to the Diftance of the virtual Focus from the Lens B G.
Hence the Sun's Rays ftriking on a Concave Lens, their Light after Refraction will be confiderably weakened j fo that the Effect of Concave-Lens's is oppofite to that of convex ones.
Zajily, An Object view'd thro' a Concave Lens, appears erect, and diminifhed in a Ratio compounded of the Ratio's of the Space in the Axis, between the Point of In- cidence, and the Point to which an oblique Ray wourd pafs without Refraction, to the Space in the Axis between the Eye and the Middle of the Object 5 and the Space in the fame Axis between the Eye and the Point of Incidence, to the Space between the Middle of the Object and the Point, the oblique Ray would pafs to without Refraction.
Tho' the Properties of Lens's have been here considered principally with regard to Rays falling near the Axis, and parallel thereto 5 yet the Reafoning will be eafily transferr'd to Rays remoter from the Axis, and falling in any Direction. Thus we may fay univcrfally, that in a Convex Leris, all parallel Rays become converging, and concur in a Focus j that diverging Rays either become ]efs diverging, or run parallel, or converge j and that con- vergingRays converge the more : All which Alterations are more fenfible in oblique Rays, than in perpendicular ones, by reafon the Angles of Incidence in that Cafe arc greater. In Concave Lens's all parallel Rays become diverging, diverging Rays diverge more ■■> converging Rays either converge lefs, or become parallel, or go out diverging : all which things hold of oblique as well as direct Rays, but more fenfibly in the firft.
